It doesn't seem like FPGA reprogramming time will be an issue. Presumably, they will work on one problem at a time. They will have a custom instruction to calculate Pi and let the machine run for a few months and then switch to crunching data from seismic oil well probes.

Modern FPGAs can be reprogrammed in a few milliseconds, which seems like a long time in the computer world. In essence megabytes of SRAM need to be written to in order to configure an FPGA.

Also, FPGAs have the ability to do partial reconfiguration, but the support is spotty. In the ideal world, parts of an FPGA would be reconfigured while the other parts were still in operation.